1. For a sample of 36 houses, what would you expect the distribution of the sale prices to be? A real-estate agent has been assigned 10 houses at random to sell his month. She wants to know whether the mean price of those houses is typical. What, if anything, does she need to assume about the distribution of prices to be able to use the Central Limit Theorem? Are those assumptions reasonable?
2. In 2008 and 2009, Systemax bought two failing electronics stores, Circuit City and CompUSA. They have kept both the names active and customers can purchase products from either webiste. If they take a random sample of a mixture of recent purchases from the two websites, the distribution of the amounts purchased will be bimodal.
a) As their sample size increases, what's the expected shape of the distribution of amounts purchased in the sample?
b) As the sample size increases, what's the expected shape of the sampling model for the mean amount purchased for the sample?